Production of monodisperse water-in-oil emulsions consisting of highly uniform droplets using asymmetric straight-through microchannel arrays

This paper reports the production of monodisperse water-in-oil (W/O) emulsions using new microchannel emulsification (MCE) devices, asymmetric straight-through MC arrays that were hydrophobically modified. The silicon asymmetric straight-through MC arrays consisted of numerous pairs of microslots and circular microholes whose cross-sectional sizes were 10 μm. This paper primarily focused on investigating the effect of the osmotic pressure of a dispersed phase (Π_d) on MCE. This paper also investigated the effects of the type of continuous-phase oils and the dispersed-phase flux (J _d) on MCE. The dispersed phases were Milli-Q water and Milli-Q water solutions containing sodium chloride. The continuous phases were decane (as control), hexane, medium chain triacylglyceride (MCT), and refined soybean oil (RSO) solutions containing tetraglycerin monolaurate condensed ricinoleic acid ester (TGCR) as a surfactant. At Π_d of exceeding threshold, highly uniform aqueous droplets with coefficients of variation of less than 3% were stably generated via hydrophobic asymmetric straight-through MCs. Monodisperse W/O emulsions with average droplet diameters between 32 and 45 μm were produced using the alkane–oil and triglyceride–oil solutions as the continuous phase. This work also demonstrated that the hydrophobic asymmetric straight-through MC array had remarkable ability to produce highly uniform aqueous droplets at very high J _d of up to 1,200 L m⁻² h⁻¹.     

Droplet coalescence by geometrically mediated flow in microfluidic channels

Microfluidic flow is geometrically mediated at a trifurcating junction allowing periodically formed, equally spaced out emulsion droplets to redistribute and fuse consistently. This is achieved by controlling the ratio between the droplet transport time across the trifurcating junction and the drainage time of the fluid volume separating the droplets t _r/t _d. Three different microfluidic trifurcation geometries have been designed and compared for their droplet fusion efficiencies. Fusion of up to six droplets has been observed in these devices. The fusion of two droplets occurs when t _r/t _d is equal to 1.25 and the number of fused droplets increases with t _r/t _d. When the junction length (d) is 216 μm fusion of 2–6 six droplets are possible however when the junction length is increased to 360 μm fusion of only two droplets is observed.     

Liquid–liquid microflows in micro-sieve dispersion devices with dual pore size

Here we present the liquid–liquid microflows and dispersion rules in micro-sieve devices with two different sized pores. The flow pattern, flux distribution and droplet size were investigated to discuss the effect of pore size deviation. Three flow patterns including dripping flow from a single active pore, dripping–dripping flow and dripping–jetting flow from two active pores were identified. A modified active pore model based on a pressure drop balance has been established. The model can predict the transition from a single active pore flow regime to a two active pore flow regime very well. In the latter regime, interactions between the small and large pores can result in dripping–dripping flow at low trans-pore flux and dripping–jetting flow at high trans-pore flux. Controlling the flow pattern in dripping–dripping flow is favorable to decreasing droplet polydispersity.     

Liquid–liquid micro-dispersion in a double-pore T-shaped microfluidic device

For further understanding the dispersion process in the T-shaped microfluidic device, a double-pore T-shaped microchannel was designed and tested with octane/water system to form monodispersed plugs and droplets in this work. The liquid–liquid two-phase flow patterns were investigated and it was found that only short plugs, relative length L/w < 1.4, were produced. Additionally, the droplets flow was realized at phase ratios (F _C /F _D) just higher than 0.5, which is much smaller than that in the single-pore T-shaped microchannels. A repulsed effect between the initial droplets was observed in the droplet formation process and the periodic fluctuation flow of the dispersed phase was discussed by analyzing the resistances. Besides, the effect of the two-phase flow rates on the plug length and the droplet diameter was investigated. Considering the mutual effect of the initial droplets and the equilibrium between the shearing force with the interfacial tension, phase ratio and Ca number were introduced into the semi-empirical models to present the plug and droplet sizes at different operating conditions.     

Effect of dispersed phase viscosity on maximum droplet generation frequency in microchannel emulsification using asymmetric straight-through channels

Uniformly sized droplets of soybean oil, MCT (medium-chain fatty acid triglyceride) oil and n-tetradecane with a Sauter mean diameter of d _3,2 = 26–35 μm and a distribution span of 0.21–0.25 have been produced at high throughputs using a 24 × 24 mm silicon microchannel plate consisting of 23,348 asymmetric channels fabricated by photolithography and deep reactive ion etching. Each channel consisted of a 10-μm diameter straight-through micro-hole with a length of 70 μm and a 50 × 10 μm micro-slot with a depth of 30 μm at the outlet of each channel. The maximum dispersed phase flux for monodisperse emulsion generation increased with decreasing dispersed phase viscosity and ranged from over 120 L m⁻² h⁻¹ for soybean oil to 2,700 L m⁻² h⁻¹ for n-tetradecane. The droplet generation frequency showed significant channel to channel variations and increased with decreasing viscosity of the dispersed phase. For n-tetradecane, the maximum mean droplet generation frequency was 250 Hz per single active channel, corresponding to the overall throughput in the device of 3.2 million droplets per second. The proportion of active channels at high throughputs approached 100% for soybean oil and MCT oil, and 50% for n-tetradecane. The agreement between the experimental and CFD (Computational Fluid Dynamics) results was excellent for soybean oil and the poorest for n-tetradecane.     

Reliable addition of reagents into microfluidic droplets

This article reports a design that reliably adds reagents into droplets by exploiting the physics of fluid flow at a T-junction in the microchannel. An expanded section right after the T-junction enhances merging of a stream with a droplet, eliminates the drawbacks such as extra droplet formation and long mixing time. The expanded section reduces the pressure buildup at the T-junction and minimizes the tendency to form extra droplets; plays the role in creating low Laplace pressure jump across the interface of the droplet forming from the T-junction which reduces the probability of forming extra droplet in the merging process; provides space for droplet coalescence if there is an extra droplet due to droplet break-up before merging. In this design, after merging, the reactants are in axial arrangement inside the droplets which lead to faster mixing. Reliable addition of reagent to the droplets happens for the combination of flow rates in a broad range from 25 to 250 μl/h, for both DI water (Q _DI) and fluorescent (Q _fluo) streams.     

Molecular simulations of droplet evaporation by heat transfer

Droplet evaporation by heat transfer is investigated by molecular dynamics simulations for a pure Lennard-Jones fluid. Two different initial conditions are treated: (1) a droplet surrounded by its vapor in equilibrium, (2) a cold droplet surrounded by warm vapor. In both cases heat is transferred from a heat bath. Results are the numbers of droplet molecules N _d and density, drift velocity, and temperature profiles as functions of time. For the small droplets considered N _d depends on the definition of a droplet molecule. The density profiles as function of time show a transition from a droplet with liquid–vapor interface to a cluster of interfacial type and finally to the gas state. The temperature at a given time is nearly constant within the droplets or clusters but strong gradients occur in the gas. In case of evaporation of a cold droplet surrounded by warm vapor we observed initially cooling down of the droplet corresponding to pressure jump evaporation and thereafter slower evaporation because of lower initial state vapor density.     

A scaling model for electrowetting-on-dielectric microfluidic actuators

A hydrodynamic scaling model of droplet actuation in an electrowetting-on-dielectric (EWD) actuator is presented that takes into account the effects of contact angle hysteresis, drag from the filler fluid, drag from the solid walls, and change in the actuation force while a droplet traverses a neighboring electrode. Based on this model, the threshold voltage, V _T, for droplet actuation is estimated as a function of the filler medium of a scaled device. It is shown that scaling models of droplet splitting and liquid dispensing all show a similar scaling dependence on [t/ε_r(d/L)]^1/2, where t is insulator thickness and d/L is the aspect ratio of the device. It is also determined that reliable operation of a EWD actuator is possible as long as the device is operated within the limits of the Lippmann–Young equation. The upper limit on applied voltage, V _sat, corresponds to contact-angle saturation. The minimum 3-electrode splitting voltages as a function of aspect ratio d/L < 1 for an oil medium are less than V _sat. However, for an air medium the minimum voltage for 3-electrode droplet splitting exceeds V _sat for d/L ≥ 0.4. EWD actuators were fabricated to operate with droplets down to 35pl. Reasonable scaling results were achieved.

Effect of viscosities of dispersed and continuous phases in microchannel oil-in-water emulsification

Although many aspects of microchannel emulsification have been covered in literature, one major uncharted area is the effect of viscosity of both phases on droplet size in the stable droplet generation regime. It is expected that for droplet formation to take place, the inflow of the continuous phase should be sufficiently fast compared to the outflow of the liquid that is forming the droplet. The ratio of the viscosities was therefore varied by using a range of continuous and dispersed phases, both experimentally and computationally. At high viscosity ratio (η _d/η _c), the droplet size is constant; the inflow of the continuous phase is fast compared to the outflow of the dispersed phase. At lower ratios, the droplet diameter increases, until a viscosity ratio is reached at which droplet formation is no longer possible (the minimal ratio). This was confirmed and elucidated through CFD simulations. The limiting value is shown to be a function of the microchannel design, and this should be adapted to the viscosity of the two fluids that need to be emulsified.     

Microchannel emulsification for mass production of uniform fine droplets: integration of microchannel arrays on a chip

We present a novel microchannel emulsification (MCE) system for mass-producing uniform fine droplets. A 60 × 60-mm MCE chip made of single-crystal silicon has 14 microchannel (MC) arrays and 1.2 × 10⁴ MCs, and each MC array consists of many parallel MCs and a terrace. A holder with two inlet through-holes and one outlet through-hole was also developed for simply infusing each liquid and collecting emulsion products. The MCE chip was sealed well by physically attaching it to a flat glass plate in the holder during emulsification. Uniform fine droplets of soybean oil with an average diameter of 10 μm were reliably generated from all the MC arrays. The size of the resultant fine droplets was almost independent of the dispersed-phase flow rate below a critical value. The continuous-phase flow rate was unimportant for both the droplet generation and the droplet size. The MCE chip enabled mass-producing uniform fine droplets at 1.5 ml h⁻¹ and 1.9 × 10⁹ h⁻¹, which could be further increased using a dispersed phase of low viscosity.     

Generating gas/liquid/liquid three-phase microdispersed systems in double T-junctions microfluidic device

This article describes the generation of microdispersed bubbles and droplets in a double T-junctions microfluidic device to form immiscible gas/liquid/liquid three-phase flowing systems. Segmented gas plugs are controllably prepared in water at the first T-junction to form gas/liquid two-phase fluid with the perpendicular flow cutting method. Then using this two-phase fluid as the cross-shearing fluid for the oil phase at the second T-junction, the gas/liquid/liquid three-phase flowing systems are prepared. Interestingly, it is found that the break-up of the oil droplets is mainly dominated by the cutting effect of the gas/liquid interface or the pressure drop across the emerging droplet, but independent with the viscous shearing effect of the continuous phase, even at the capillary number (Ca = u _wμ_w/γ_ow) higher than 0.01. The size laws and the distributions of the bubbles and droplets are investigated carefully, and a mathematical model has been developed to relating the operating conditions with the dispersed sizes.     

Droplet generation in a microchannel with a controllable deformable wall

We report the droplet generation behavior of a microfluidic droplet generator with a controllable deformable membrane wall using experiments and analytical model. The confinement at the droplet generation junction is controlled by using external pressure, which acts on the membrane, to generate droplets smaller than junction size (with other parameters fixed) and stable and monodispersed droplets even at higher capillary numbers. A non-dimensional parameter, i.e., controlling parameter K _p, is used to represent the membrane deformation characteristics due to the external pressure. We investigate the effect of the controlled membrane deformation (in terms of K _p), viscosity ratio λ and flow rate ratio r on the droplet size and mobility. A correlation is developed to predict droplet size in the controllable deformable microchannel in terms of the controlling parameter K _p, viscosity ratio λ and flow rate ratio r. Due to the deflection of the membrane wall, we demonstrate that the transition from the stable dripping regime to the unstable jetting regime is delayed to a higher capillary number Ca (as compared to rigid droplet generators), thus pushing the high throughput limit. The droplet generator also enables generation of droplets of sizes smaller than the junction size by adjusting the controlling parameter.     

Microfluidic architectures for efficient generation of chemistry gradations in droplets

We demonstrate a strategy for construction of high-throughput microfluidic systems generating gradations of chemistry in micro-droplets. The productivity of the systems that we propose is limited only by the maximum rate of the droplet formation, and does not need to be limited by the rate of mixing. Multilayer polycarbonate chips transform two miscible input streams A and B into N streams of droplets, containing mixtures [A] _i , [B] _i . Exemplary devices generate linear ([B] _i  ∝ i) and logarithmic gradations (ln[B] _i  ∝ i). We also analyze the use of the same strategy for the generation of concentration gradation in the streams of droplets comprising mixtures of liquids of different viscosities. The devices preserve the required distribution of compositions, while allowing the volume of the droplets to be tuned over almost two orders of magnitude (i.e. between 3 and 80 nL).     

Droplets coalescence and mixing with identical and distinct surface tension on a wettability gradient surface

The influence of identical and distinct surface tensions on the coalescence and mixing of droplets after a direct collision on a wettability gradient surface (made from a self-assembled monolayer, SAM technique) was investigated. The results indicate that their mixing is driven sequentially by interior convection and diffusion; the convection endures less than 100 ms but dominates more than 60 % of the mixing. If the stationary droplet has a large surface tension (73.28 mN × m^?1), whether the moving droplet has a large surface tension (73.28 mN × m^?1) or a small surface tension (38.63 mN × m^?1), the mushroom-shaped mixing pattern is generated within the coalesced droplet that enhances the convective mixing and also significantly enlarges the interface for mass diffusion. The mixing index of these two cases was greater than 0.8 at 120 s after the collision. For the cases in which the stationary droplet with a small surface tension collided by the moving droplet with a large surface tension, a mixing pattern with a round-head shape developed, which was insufficient to benefit the mixing. When the stationary and moving droplets both had small surface tension, the moving droplet was unable to merge with stationary droplet and had poor mixing quality due to the small surface Gibbs energy of both stationary and moving droplets. For the collision of droplets of identical surface tension, the surface tension affects the coalescence behavior; for the collision of droplets with distinct surface tension, the coalescence behavior and mixing quality depend on the colliding arrangement of stationary and moving droplets.     

Panconnectivity and edge-pancyclicity of 3-ary <Emphasis Type="Italic">N</Emphasis>-cubes

We study two topological properties of the 3-ary n-cube Q _n ³. Given two arbitrary distinct nodes x and y in Q _n ³, we prove that there exists an x–y path of every length ranging from d(x,y) to 3 ⁿ −1, where d(x,y) is the length of a shortest path between x and y. Based on this result, we prove that Q _n ³ is edge-pancyclic by showing that every edge in Q _n ³ lies on a cycle of every length ranging from 3 to 3 ⁿ .

Scale-up and control of droplet production in coupled microfluidic flow-focusing geometries

A single microfluidic chip consisting of six microfluidic flow-focusing devices operating in parallel was developed to investigate the feasibility of scaling microfluidic droplet generation up to production rates of hundreds of milliliters per hour. The design utilizes a single inlet channel for both the dispersed aqueous phase and the continuous oil phase from which the fluids were distributed to all six flow-focusing devices. The exit tubing for each of the six flow-focusing devices is separate and individually plumbed to each device. Within each flow-focusing device, the droplet size was monodisperse, but some droplet size variations were observed across devices. We show that by modifying the flow resistance in the outlet channel of an individual flow-focusing device it is possible to control both the droplet size and frequency of droplet production. This can be achieved through the use of valves or, as is done in this study, by changing the length of the exit tubing plumbed to the outlet of the each device. Longer exit tubing and larger flow resistance is found to lead to larger droplets and higher production frequencies. The devices can thus be individually tuned to create a monodisperse emulsion or an emulsion with a specific drop size distribution.     

Approximate Range Searching in External Memory

In this paper, we present two linear-size external memory data structures for approximate range searching. Our first structure, the BAR-B-tree, stores a set of N points in ℝ ^d and can report all points inside a query range Q by accessing O(log  _B N+ε ^γ +k _ε /B) disk blocks, where B is the disk block size, γ=1−d for convex queries and γ=−d otherwise, and k _ε is the number of points lying within a distance of ε⋅diam (Q) to the query range Q. Our second structure, the object-BAR-B-tree, is able to store objects of arbitrary shapes of constant complexity and provides similar query guarantees. In addition, both structures can support other types of range searching queries such as range aggregation and nearest-neighbor. Finally, we present I/O-efficient algorithms to build these structures.     

On one application of computations with oracle

Let P(d) be a program implementing a partial recursive function φ. Let $ \mathcal{O} $ \mathcal{O} _P denote a function defined on the domain of function φ that maps an input data d ₀ onto the path of computation of P on the input d ₀. Let Q(p, d) be a program returning a value if and only if p = $ \mathcal{O} $ \mathcal{O} _P (d), and let the value of the program be Q($ \mathcal{O} $ \mathcal{O} _P (d), d) = P(d). Program Q(p, d), which is totally absurd from the point of view of its practical computation on concrete input data, may be practically useful when it is analyzed by a metaprogram. It is shown in the paper how program Q(p, d) can be used for verification of a postcondition imposed on program P(d). The proposed method was tested on verification tasks for cache coherence protocols and other distributed computing systems.     

Monodispersed water-in-oil emulsions prepared with semi-metal microfluidic EDGE systems

Monodispersed water-in-oil emulsions were prepared with EDGE (Edge based Droplet GEneration) systems, which generate many droplets simultaneously from one junction. The devices (with plateau height of 1.0 μm) were coated with Cu and CuNi having the same hydrophobicity but different surface roughness. Emulsification was performed by using water as dispersed phase and oils with different viscosities (hexadecane, decane, hexane and sunflower oil) as continuous phases; lecithin, polyglycerol polyricinoleate (PGPR) and span80 were used as emulsifiers. The roughness affected the emulsification behaviour significantly. The smoother Cu surface exhibited droplet formation over the entire length of the droplet formation unit, while the rougher CuNi surface showed non-uniform filling of the plateau and much lower droplet formation frequency. In spite of this different behaviour, monodispersed droplets (CV <10 %) were produced by both systems (with span80 and PGPR), with a size six times the plateau height (d _avg ≈ 6.0 μm). The droplet size decreased with increasing viscosity ratio and remained constant above some critical value. The emulsification process was stable over a wider range of pressures as previously found for silicon-based systems. The amount of PGPR influenced the pressure stability, but the system could be used effectively, while with lecithin and span80 the stable pressure range was very small. The pressure and viscosity stability of these semi-metal systems with rough surfaces show that the EDGE system has potential for practical applications, especially since overall productivity is not affected.